Multi-objective Optimization with Fuzzy Based Ranking for TCSC Supplementary Controller to Improve Rotor Angle and Voltage Stability

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1 International Journal o lectrical an lectronics ngineering 3:9 9 Multi-obective Optimization with Fuzzy Base Ranking or CSC Supplementary Controller to Improve Rotor Angle an oltage Stability S. Pana, S. C. Swain, A. K. Baliarsingh, A. K. Mohanty an C. Aril Abstract Many real-worl optimization problems involve multiple conlicting obectives an the use o evolutionary algorithms to solve the problems has attracte much attention recently. his paper investigates the application o multi-obective optimization techniue or the esign o a hyristor Controlle Series Compensator (CSC)-base controller to enhance the perormance o a power system. he esign obective is to improve both rotor angle stability an system voltage proile. A Genetic Algorithm (GA) base solution techniue is applie to generate a Pareto set o global optimal solutions to the given multi-obective optimisation problem. Further, a uzzy-base membership value assignment metho is employe to choose the best compromise solution rom the obtaine Pareto solution set. Simulation results are presente to show the eectiveness an robustness o the propose approach. Keywors Multi-obective Optimisation, hyristor Controlle Series Compensator, Power System Stability, Genetic Algorithm, Pareto Solution Set, Fuzzy Ranking. P I. INRODUCION OWR system oscillations an system voltage proile are the two important criteria which eine the perormance o a power system subecte to a isturbance []. here has been much research interest in eveloping new control methoologies or increasing the perormance o the power system. Recent evelopment o power electronics introuces the use o Flexible AC ransmission Systems (FACS) controllers in power systems. hyristor Controlle Series Compensator (CSC) is one o the important members o FACS amily that is increasingly applie with long transmission lines by the utilities in moern power systems [- 8]. he maority o the control methoologies presente in literature concerns improvement o only one type o stability S. Pana is working as a Proessor in the Department o lectrical an lectronics ngineering, NIS, Berhampur, Orissa, Inia, Pin: 768. ( panasihartha@reimail.com ). S. Swain is working as an Assistant Proessor in the lectrical ngineering Department, School o echnology, KII University, Bhubaneswar, Orissa, Inia (e mail:scs3@reimail.com). A.K.Baliarsingh is a Research Scholar in the lectrical ngineering Department, School o echnology, KII University, Bhubaneswar, Orissa, Inia ( scs3@reimail.com). A. K. Mohanty is an x-proessor in N. I.. Rourkela. now working as a Proessor in lectrical ngg. Deptt. at KII UNIRSIY Bhubaneswar C. Aril is with National Acaemy o Aviation, AZ5, Baku, Azerbaian, Bina, 5th km, NAA ( cemalaril@gmail.com). perormance; either improving the oscillatory stability perormance (relecte in the eviation in generator spee) or the system voltage proile an imization o a single obective unction is employe to get the esire perormance. Multi-obective genetic algorithm approach has been applie to esign a CSC controller [9], where the three obectives are closely relate an the voltage eviations are not taken into account. Further, the proceure to obtain the best compromise solution rom the obtaine Pareto set is not aresse. Obviously, the main purpose o esign o any controller is to enable it to improve both oscillatory stability an system voltage proile. Design o such kin o controller is inherently a multi-obective optimisation problem. here are two general approaches to multiple obective optimisations. One approach to solve multi-obective optimisation problems is by combining the multiple obectives into a scalar cost unction, ultimately making the problem single-obective prior to optimisation. However, in practice, it can be very iicult to precisely an accurately select these weights as small perturbations in the weights can lea to very ierent solutions. Further, i the inal solution oun cannot be accepte as a goo compromise, new runs o the optimiser on moiie obective unction using ierent weights may be neee, until a suitable solution is oun. hese methos also have the isavantage o reuiring new runs o the optimiser every time the preerences or weights o the obectives in the multi-obective unction change []. he secon general approach is to etere an entire Pareto optimal solution set or a representative subset. Pareto optimal solution sets are oten preerre to single solutions because they can be practical when consiering real-lie problems, since the inal solution o the ecision maker is always a trae-o between crucial parameters []. he main motivation or using Genetic Algorithm (GA) to solve multi-obective optimisation problems is because GAs eal simultaneously with a set o possible solutions (the socalle population) which allows the user to in several members o the Pareto optimal set in a single run o the algorithm, instea o having to perorm a series o separate runs as in the case o the traitional mathematical programg techniues. he Pareto optimal solutions are ones within the search space whose corresponing obective vector components cannot be improve simultaneously. Aitionally, GAs are less susceptible to the shape or continuity o the Pareto ront as they can easily eal with 5

2 International Journal o lectrical an lectronics ngineering 3:9 9 iscontinuous an concave Pareto ronts, whereas these two issues are known problems with mathematical programg []. In this paper, the esign problem o a CSC is ormulate as a multi-obective optimisation problem. GA base multiobective optimisation metho is aapte or generating Pareto solutions in esigning a CSC-base controller. he esign obective is to improve the oscillatory stability an system voltage proile o a power system ollowing a isturbance. Further a uzzy base membership unction value assignment metho is employe to choose the best compromise solution rom the obtaine Pareto set. Simulation results are presente at various loaing conitions to show the eectiveness an robustness o the propose approach. he reer o the paper is organize in ive maor sections. Power system moeling with the propose CSCbase supplementary amping controller is presente in Section II. he propose esign approach an the obective unction are presente in section III. In Section I, an overview o multi-obective optimization gas been presente. he results are presente an iscusse in Section. Finally, in Section I conclusions are given. II. MODLING H POWR SYSM WIH CSC he single-machine ininite-bus (SMIB) power system installe with a CSC, shown in Figure is consiere in this stuy. In the igure, an L represent the reactance o the transormer an the transmission line respectively; an B are the generator teral an ininite bus voltage respectively. CSC is one o the most important an best known FACS evices, which has been in use or many years to increase line power transer as well as to enhance system stability. Basically, a CSC consists o three main components: capacitor bank C, bypass inuctor L an biirectional thyristors SCR an SCR. he iring angles o the thyristors are controlle to aust the CSC reactance in accorance with a system control algorithm, normally in response to some system parameter variations. Accoring to the variation o the thyristor iring angle or conuction angle, this process can be moele as a ast switch between corresponing reactance oere to the power system. Generator L P C C CSC L Fig. Single machine ininite bus power system with CSC B Ininite bus A. Non-Linear uations he non-linear ierential euations o the SMIB system with CSC are erive by neglecting the resistances o all components o the system (generator, transormer an transmission lines) an the transients o the transmission lines an transormer. he non-linear ierential euations are [3]: b () [ P m P e ] () M where, Pe o [ K A s B ( R A [ R ] ] B ( ) sin sin B sin L + ( B ) CSC, () K A sa ) cos B cos Fig. Simpliie I type S A excitation system (3) () (5) 55

3 International Journal o lectrical an lectronics ngineering 3:9 9 he simpliie I ype-sa excitation system is consiere in this work. he iagram o the I ype-sa excitation system is shown in Fig.. he inputs to the excitation system are the teral voltage an reerence voltage R. he gain an time constants o the excitation system are represente by K A an A respectively. B. Linearize uations In the esign o electromechanical moe amping stabilizer, a linearize incremental moel aroun an operating point is usually employe. he Phillips-Heron moel o the power system with FACS evices is obtaine by linearizing the set o euations () (5) aroun an operating conition o the power system. he linearize expressions are as ollows: b (6) P / [ K K K D ] M (7) [ K 3 K K Q ]/ [ K A ( K 5 K 6 K ) ]/ where, K P K P, K P e, e A P e K 3, K, KQ K K, K 5, 6 he moiie Phillips-Heron moel o the singlemachine ininite-bus (SMIB) power system with CSC-base amping controller is obtaine using linearize euations (6)- (9) as shown in Fig. 3. P m + K MsD K P K 3 s o K GCSC(s) K Q K 6 K + s K A sa K K 5 (8) (9) + Fig. 3 Moiie Phillips-Heron moel o SMIB with CSC-base supplementary amping controller S III. H PROPOSD APPROACH A. Structure o Propose CSC-base Supplementary Damping Controller he commonly use lea lag structure is chosen in this stuy as CSC-base supplementary amping controller as shown in Fig.. he structure consists o a gain block; a signal washout block an two-stage phase compensation block. he phase compensation block provies the appropriate phase-lea characteristics to compensate or the phase lag between input an the output signals. he signal washout block serves as a high-pass ilter which allows signals associate with oscillations in input signal to pass unchange. Without it steay changes in input woul moiy the output. Input K Gain Block sw s sw s Washout Block G CSC ( s ) s3 s wo stage lea-lag Block Fig.. Structure o the propose CSC-base supplementary amping controller Output he amping torue contribute by the CSC can be consiere to be in to two parts. he irst part K P, which is reerre as the irect amping torue, is irectly applie to the electromechanical oscillation loop o the generator. he secon part K Q an K, name as the inirect amping torue, applies through the iel channel o the generator. he amping torue contribute by CSC controller to the electromechanical oscillation loop o the generator is: K K K () D D he transer unctions o the CSC controller is: u CSC K P sw s w D s s s s 3 y () Where, u CSC is the output signal o CSC controller an y is the input signal. he input signal o the propose CSCbase controller is the spee eviation an the output is the change in conuction angle. During steay state conitions = an so the eective reactance is given by: L CSC ( ). During ynamic conitions the series compensation is moulate or amping system oscillations. he eective reactance in ynamic conitions is given by: L CSC ( ), where an ( ), an being initial value o iring an conuction angle respectively. From the viewpoint o the washout unction the value o washout time constant is not critical in lea-lag structure 56

4 International Journal o lectrical an lectronics ngineering 3:9 9 controllers an may be in the range to secons []. In the present stuy, washout time constant o W s is use. he controller gains K ; an the time constants,, 3 an are to be etere. B. Obective Function It is worth mentioning that the CSC controller is esigne to amp power system oscillations an improve the system voltage proile ater a isturbance. A multi-obective unction base on an is use as an obective unction in the present stuy. he obective can be ormulate as the imisation o unction F given by: F F, F () Where, an t t. t. F. t. t (3) F t () In the above euations, an enote the absolute values o rotor spee an teral voltage eviations ollowing a isturbance an t is the time range o the simulation. For the obective unction calculation, the timeomain simulation o the power system moel is carrie out or the simulation perio. C. Optimization Problem In this stuy, it is aime to imize the propose obective unctions F. he problem constraints are the CSC Controller parameter bouns. hereore, the esign problem can be ormulate as the ollowing optimization problem: Minimize F (5) Subect to K K K (6) (7) (8) (9) () he propose approach employs genetic algorithm to solve this optimization problem an search or optimal set o the CSC Controller parameters. I. MULI-OBJCI OPIMIZAION A. Multi-obective optimization A multi-obective optimization problem (MOP) iers rom a single-obective optimization problem because it contains several obectives that reuire optimization. In case o single obective optimization problems, the best single esign solution is the goal. But or multi-obective problems, with several an possibly conlicting obectives, there is usually no single optimal solution. hereore, the ecision maker is reuire to select a solution rom a inite set by making compromises. A suitable solution shoul provie or acceptable perormance over all obectives. A general ormulation o a MOP consists o a number o obectives with a number o ineuality an euality constraints. Mathematically, the problem can be written as []: imise/imise i (x) or i =,,,n. () Subect to constraints: g (x) h k (x) =,,, J k =,,, K Where i (x) = { (x), n (x)} n = number o obectives or criteria to be optimize x = {x,, x p } is a vector o ecision variables p = number o ecision variables here are two approaches to solve the MOP. One approach is the classical weighte-sum approach where the obective unction is ormulate as a weighte sum o the obectives. But the problem lies in the correct selection o the weights or utility unctions to characterise the ecision-makers preerences. In orer to solve this problem, the secon approach calle Pareto-optimal solution can be aapte. he MOPs usually have no uniue or perect solution, but a set o non-oate, alternative solutions, known as the Paretooptimal set. Assug a imisation problem, oance is eine as ollows: A vector u = (u,.,u n ) is sai to oate v = ( v,..,v n ) i an only i u is partially less than v ( u p< v), i {,,n}, u i v i i {,,n}; u i < v i () A solution x u U is sai to be Pareto-optimal i an only i there is no x v U or which v = (x v ) = (v,,v n ) oates u = (x u ) = ( u,,u n ). B. Pareto-optimal solutions Pareto-optimal solutions are also calle eicient, nonoate, an non-inerior solutions. he corresponing obective vectors are simply calle non-oate. he set o all non-oate vectors is known as the non-oate set, or the trae-o surace, o the problem. A Pareto optimal set is a set o solutions that are non-oate with respect to each other. While moving rom one Pareto solution to another, there is always a certain amount o sacriice in one obective to achieve a certain amount o gain in the other. he elements in the Pareto set has the property that it is impossible to urther reuce any o the obective unctions, without increasing, at least, one o the other obective unctions. 57

5 International Journal o lectrical an lectronics ngineering 3:9 9 Pareto-optimal solutions are also calle eicient, nonoate, an non-inerior solutions. he corresponing obective vectors are simply calle non-oate. he set o all non-oate vectors is known as the non-oate set, or the trae-o surace, o the problem. A Pareto optimal set is a set o solutions that are non-oate with respect to each other. While moving rom one Pareto solution to another, there is always a certain amount o sacriice in one obective to achieve a certain amount o gain in the other. he elements in the Pareto set has the property that it is impossible to urther reuce any o the obective unctions, without increasing, at least, one o the other obective unctions. C. GA metho or generating Pareto solutions he ability to hanle complex problems, involving eatures such as iscontinuities, multimoality, isoint easible spaces an noisy unction evaluations reinorces the potential eectiveness o GA in optimisation problems. Although, the conventional GA is also suite or some kins o multiobective optimisation problems, it is still iicult to solve those multi-obective optimisation problems in which the iniviual obective unctions are in the conlict conition. Gen. = Gen. + Apply GA opterators (selection, crossover an mutation) Start Initialize population an Pareto optimal set Gen. = ime-omain simulation o power system moel Obective unction evaluation Obtain Pareto solution set Pareto size >. size? No Gen. >. Gen.? No Yes Yes Fig. 5 Flowchart o the multi-obective genetic algorithm optimization algorithm to generate Pareto solutions Reuce Pareto optimal set size Stop Being a population base approach; GA is well suite to solve MOPs. A generic single-obective GA can be easily moiie to in a set o multiple non-oate solutions in a single run. he ability o GA to simultaneously search ierent regions o a solution space makes it possible to in a iverse set o solutions or iicult problems with nonconvex, iscontinuous, an multi-moal solutions spaces. he crossover operator o GA exploits structures o goo solutions with respect to ierent obectives to create new nonoate solutions in unexplore parts o the Pareto ront. In aition, most multi-obective GA oes not reuire the user to prioritise, scale, or weigh obectives. hereore, GA has been the most popular heuristic approach to multi-obective esign an optimization problems. Pareto-base itness assignment was irst propose by Golberg [5], the iea being to assign eual probability o reprouction to all non-oate iniviuals in the population. he metho consiste o assigning rank to the non-oate iniviuals an removing them rom contention, then ining a new set o non-oate iniviuals, ranke, an so orth. In the present stuy, beore ining the Pareto-optimal iniviuals or the current generation, the Pareto-optimal iniviuals rom the previous generation are ae. he computational low chart o the propose multi-obective optimization algorithm is shown in Fig. 5.. RSULS AND DISCUSSIONS A. Application o Genetic Algorithm he obective unction given by euation () is evaluate by simulating the system ynamic moel consiering a % step increase in mechanical power input (P m ) at t =. sec. Optimization is terate by the prespeciie number o generations. While applying GA, a number o parameters are reuire to be speciie. An appropriate choice o the parameters aects the spee o convergence o the algorithm. able I shows the speciie parameters or the GA algorithm. One more important actor that aects the optimal solution more or less is the range or unknowns. ABL IPARAMRS USD IN MULI-OBJCI GNIC ALGORIHM Parameter alue/ype Maximum generations Population size 5 Mutation rate. Selection operator Pareto-optimal sorting Recombination operator ype o selection Blening Pareto optimal selection For the very irst execution o the program, a wier solution space can be given an ater getting the solution one can shorten the solution space nearer to the values obtaine in the previous iteration. he inal Pareto solution surace is shown in Fig. 6 where the Pareto solutions are shown with the marker o. B. Best Compromise Solution In the present paper, a Fuzzy-base approach is applie to select the best compromise solution rom the obtaine Pareto set. he -th obective unction o a solution in a Pareto set 58

6 International Journal o lectrical an lectronics ngineering 3:9 9 Fitness o F Fintess o F Fig. 6 Pareto solution surace It is clear rom able III that the open loop system is unstable at all the loaing conitions because o negative amping o electromechanical moe (s =.655,.78,.86 or noal, light an heavy loaing respectively). Without optimize CSC controller parameters the system stability is maintaine as the electromechanical moe eigenvalue shit to the let o the line in s-plane (s = -.8, -.88, -.88 or noal, light an heavy loaing respectively) or all loaing conitions. It is also clear that optimize CSC controller shits substantially the electromechanical moe eigenvalue to the let o the line (s = , , or noal, light an heavy loaing respectively) in the s-plane, which enhances the system stability an improves the amping characteristics o electromechanical moe. is represente by a membership unction eine as [6]:,, (), where an are the imum an imum values o the -th obective unction, respectively. For each solution i, the membership unction calculate as: n i is i i (3) m n i i where, n is the number o obectives unctions an m is the number o solutions. he solution having the imum value i o is the best compromise solution. Using the above approach the best compromise solution is obtaine as: K = , =.68 s, =.637 s, 3 =.36 s an =.36 s C. igenvalue Analysis o assess the eectiveness an robustness o the propose stabilizers, three ierent loaing conitions given in able II are consiere. he system electromechanical moe eigenvalues without an with the propose controllers are shown in able III. able III also shows the system electromechanical eigenvalues without optimize CSC controller parameters. In this case the values are ranomly chosen as: K =, =. s, =.5 s, 3 =.5 s an =.5 s. Loaing Conitions Noal loaing Light loaing Heavy loaing ABL II LOADING CONDIIONS CONSIDRD P Q Loaing conitions (eg.) Noal loaing Light loaing Heavy loaing ABL III SYSM LCROMCHANICAL MOD IGNALUS Without control i i i D. Simulation Results Without optimize CSC i i i With optimize CSC i i i In orer to veriy the eectiveness o the propose approach, the perormance o the optimize CSC controller is teste or ierent loaing conitions an compare with the case where the CSC-base controller parameters are not optimize (i.e. using the ranomly chosen values as the CSC-base controller parameters). A % step increase in mechanical power input at t =. sec is consiere. he response with CSC without optimization are shown in otte lines (with legen ); an the responses with optimize CSC controllers are shown with soli lines (with legen ). he system is unstable without control or the above contingency an the responses are not shown in igures. he system spee eviation an teral voltage response or the above contingency at all the loaing conition are shown in Figs. 7 an 8 respectively. hese simulation results illustrate the eectiveness an robustness o propose esign approach. It is clear that the propose CSC controller has goo amping characteristics to low reuency oscillations an stabilizes the system uickly or all loaing conitions. 59

7 International Journal o lectrical an lectronics ngineering 3:9 9 x x ime (sec) (a) Noal loaing ime (sec) (a) Noal loaing x - 5 x ime (sec) (b) Light loaing ime (sec) (b) Light loaing x ime (sec) (c) Heavy loaing Fig. 7 Spee eviation responses or a % step increase in mechanical power input (a) noal loaing (b) light loaing (c) heavy loaing. I. CONCLUSIONS In this stuy, the perormance improvement o a power system by optimal esign o a CSC-base controller is presente an iscusse. he esign obective is to improve both rotor angle stability an system voltage proile. A Genetic Algorithm (GA) base solution techniue is applie to generate a Pareto set o global optimal solutions to the given multi-obective optimisation problem. Further, a uzzy-base membership value assignment metho is employe to choose the best compromise solution rom the obtaine Pareto solution set. igenvalue analysis an simulation results are ime (sec) (c) Heavy loaing Fig. 8 eral voltage responses or a % step increase in mechanical power input (a) noal loaing (b) light loaing (c) heavy loaing. presente uner various loaing conitions to show the eectiveness an robustness o the propose approach.he propose metho is valuable or the esign o the interactive ecision making. he ecision makers can choose rom the solutions in the Pareto-optimal set to in out the best solution accoring to the reuirement an nees as the esire parameters o their controllers. he results show that evolutionary algorithms are eective tools or hanling multiobective optimization where multiple Pareto-optimal solutions can be oun in one simulation run. 55

8 International Journal o lectrical an lectronics ngineering 3:9 9 RFRNCS [] P. Kunur, Power System Stability an Control, McGraw-Hill, 99 [] A. D Del Rosso, C. A Canizares an.m. Dona, A stuy o CSC controller esign or power system stability improvement, I rans. Power Systs., vol-8, pp [3] S. Pana, N. P. Pahy, R. N. Patel Moeling, simulation an optimal tuning o CSC controller, International Journal osimulation Moelling. ol. 6, No., pp. 7-8, 7. [] S. Pana, an N. P. Pahy Comparison o Particle Swarm Optimization an Genetic Algorithm or FACS-base Controller Design, Applie Sot Computing. ol. 8, pp. 8-7, 8. [5] S. Pana, S. C. Swain, A. K. Baliarsingh, C. Aril, Optimal Supplementary Damping Controller Design or CSC mploying RCGA, International Journal o Computational Intelligence, ol. 5, No., pp. 36-5, 9. [6] Sihartha Pana an Narayana Prasa Pahy, Application o Genetic Algorithm or PSS an FACS base Controller Design, International Journal o Computational Methos, ol. 5, Issue, pp. 67-6, 8. [7] S. Pana an R.N.Patel, Damping Power System Oscillations by Genetically Optimize PSS an CSC Controller International Journal o nergy echnology an Policy, ol. 5, No., pp. 57-7, 7. [8] S. Pana, N.P.Pahy an R.N.Patel, Robust Coorinate Design o PSS an CSC using PSO echniue or Power System Stability nhancement, Journal o lectrical Systems, ol. 3, No., pp. 9-3, 7. [9] Sihartha Pana, N.P.Pahy, hyristor Controlle Series Compensatorbase Controller Design mploying Genetic algorithm: A Comparative Stuy International Journal o lectronics, Circuits an Systems, ol., No., pp. 38-7, 7. [] C. A.C. Coello, A comprehensive survey o evolutionary-base multiobective optimization techniues, Knowlege an Inormation Systems, ol., No. 3, pp , 999. []. Chankong an Y. Haimes, Multiobective Decision Making heory an Methoology, New York: North-Hollan [] C. M Fonseca, an P. J. Fleg, Genetic algorithms or multiobective optimization: ormulation, iscussion an generalization, Proceeings o the Fith International Conerence on Genetic Algorithms, San Mateo Caliornia. pp. 6-3, 993. [3] H. F. Wang, F. J. Swit, A Uniie Moel o FACS Devices in Damping Power System Oscillations Part-: Single-machine Ininite-bus Power Systems, I rans. Power Delivery, ol., No., pp. 9-96, 997. [] S. S. Rao, Optimization heory an Application,New Delhi: Wiley astern Limite, 99. [5] D.. Golberg, Genetic Algorithms in Search, Optimization, an Machine Learning, Aison-Wesley, 989. [6] Sihartha Pana Multi-obective evolutionary algorithm or SSSCbase controller esign, lectric Power System Research., ol. 79, Issue 6, pp , 9. Inia. He is working towars his PhD in KII University in the area o Application o Computational Intelligent echniues to Power System Stability Problems an Flexible AC ransmission Systems controller esign. Dr. A. K. Mohanty is an x-proessor in N.I..Rourkela.Now he is working as a Proessor in lectrical ngg. Deptt. at KII UNIRSIY Bhubaneswar. Cemal Aril is with National Acaemy o Aviation, AZ5, Baku, Azerbaian, Bina, 5th km, NAA Sihartha Pana is a Proessor at National Institute o Science an echnology, Berhampur, Orissa, Inia. He receive the Ph.D. egree rom Inian Institute o echnology, Roorkee, Inia in 8, M.. egree in Power Systems ngineering in an B.. egree in lectrical ngineering in 99. arlier he worke as Associate Proessor in KII University, Bhubaneswar, Inia an IAM College o ngineering, Anhra Praesh, Inia an Lecturer in the Department o lectrical ngineering, SMI, Orissa, Inia.His areas o research inclue power system transient stability, power system ynamic stability, FACS, optimization techniues, istribute generation an win energy. S. C. Swain receive his M.. egree rom UC Burla in. Presently he is working as an Assistant Proessor in the Department o lectrical ngineering, School o technology, KII,University, Bhubaneswar, Orissa, Inia. He is working towars his PhD in KII University in the area o Application o Computational Intelligent echniues to Power System. A. K. Baliarsingh is working as an Assistant Proessor in the Department o lectrical ngineering, Orissa ngineering College, Bhubaneswar, Orissa, 55